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SUMMARYVariations of the latent semantic indexing (LSI) method in information retrieval (IR) require the computation of singular subspaces associated with the k dominant singular values of a large m × n sparse matrix A, where k min(m; n). The Riemannian SVD was recently generalized to low-rank matrices arising in IR and shown to be an e ective approach for formulating an enhanced semantic model that captures the latent term-document structure of the data. However, in terms of storage and computation requirements, its implementation can be much improved for large-scale applications. We discuss an ecient and reliable algorithm, called SPK-RSVD-LSI, as an alternative approach for deriving the enhanced semantic model. The algorithm combines the generalized Riemannian SVD and the Lanczos method with full reorthogonalization and explicit restart strategies. We demonstrate that our approach performs as well as the original low-rank Riemannian SVD method by comparing their retrieval performance on a well-known benchmark document collection.

Background There is no consensus on the optimal management of clavicle fractures, with advocates of both operative and non‐operative management. The objective of this study is to assess the trends in the management of clavicle fractures in Australia over the past two decades. Methods The incidence of surgical fixation of clavicle fractures from 2001 to 2020 was analysed using the Australian Medicare Benefits Schedule database, reflective of operations performed on privately insured patients, thus excluding public patients and compensable cases. An offset term was utilized with data from the Australian Bureau of Statistics to account for population changes over the study period. Results A total of 17 089 procedures for the management of clavicle fractures were performed from 2001 to 2020. The incidence of operative intervention increased from 1.87 per 100 000 in 2001 to a peak of 6.63 per 100 000 in 2016. An overall increase was seen in males (310%) and females (347%) over the study period, as well as across all age groups. A greater proportion of operative interventions was performed on males (n = 14 075, 82%) than females (n = 3014, 18%, P < 0.001). The greatest increase in intervention was noted in those aged 65 or older (14% increase per year, 95% CI 11%–17%, P < 0.05). In 2020, the incidence of operative intervention decreased to a level last seen in 2013. Conclusions The incidence of operative interventions for clavicle fractures has increased in Australia over the 20‐year study period. This increase is in keeping with recent evidence suggesting several advantages when displaced mid‐shaft clavicle fractures are operatively managed.

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